I consider that, it should be the type-0. This type is represented by Turing machine. I think, that it is because of the dynamic changing tokens during runtime, dynamic changing of the meaning of macros, calculating Lambda calcul (what should be the most important).

There is a proof that LaTeX is Turing complete here. I obtained the link from Antal S-Z's answer explaining why TeX cannot have a BNF grammar. Not sure if this answer might be helpful.
– user79242May 30 '15 at 23:29